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Leah's answering machine receives about six calls between 8 a.m. and 10 a.m., a two-hour window. Rescaled to μ = 0.75 calls per 15 minutes, X ~ P(0.75). What is P(x>1), the chance of more than one call in the next 15 minutes?
A0.1734
B0.75
C0.8266
D0.25
Answer & Solution
Correct answer: A. 0.1734
1. Six calls in 2 hours gives (1/8)(6) = 0.75 calls per 15-minute interval, so X ~ P(0.75).
2. Using a calculator, P(x>1) = 1 - poissoncdf(0.75, 1).
3. That evaluates to about 0.1734.
4. Option C is the complement of the correct answer, P(x≤1), not P(x>1) itself.
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 4 "Discrete Random Variables", section 4.6 Poisson Distribution_
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